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What do health insurance and all-you-can-eat buffets have in common? The economic theory of adverse selection tells us that neither should exist.

Consider the case of Bill Wisth. Bill is six-and-a-half feet tall, 350 pounds, and as you can see in the amusing news story below, he's been kicked out of an all-you-can-eat fried fish buffet. What's surprising is not that this happened, but that it doesn't happen more often (ok, it's also a little surprising that Bill has decided to picket the restaurant). I will explain, but first, watch the video:

So why should this happen more often? When someone offers all-you-can-eat to any customers, those that show up should be ones for whom the amount that they can eat is worth more than the price they expect to pay. After all, if the buffet costs $10 no matter how much you eat then those who eat the most will get the most value out of it. But the average amount consumed can't exceed the price, otherwise the restaurant will lose money and go out of business. So if the average amount consumed is $16 worth of food, then the restaurant will have to raise the price to above $16. But this means those who more than $10 but less than $16 worth of food will no longer find it worthwhile to eat there, so they will stop going, and the average customer left will be those who eat more than $16 worth.

This process continues, until there is only one guy left going to the buffet, and he eats $300 worth of fish and is charged exactly $300 for it. In effect, this theory says that all-you-can-eat buffets should not exist. And yet they do, and for the most part the adverse selection problem does not cause problems. Except, it seems, for Bill Witsh.

The theory of adverse selection was first applied by George Ackerlof to the market for used cars in the 1970s. The real issue is that buyers and sellers have asymmetrical information. In the buffet example the asymmetric information is that the restaurant can't tell who is going to eat a ton of fried fish and who isn't. Which means they can't screen out guys like Bill Wisth in advance. Perhaps the most famous and common application of adverse selection theory is in health insurance. Here you have insurers who can't observe how risky their customers are, and thus everyone is charged the same. Just as in the buffet case, those who will buy the insurance are those with the greatest expected health care costs and in particular those for whom the expected costs of health care exceed the cost of the insurance. Left unable to charge risky customers for high expected costs of insuring, or screen them out all together, the insurer is flooded with costly customers and so must raise prices. This sets off a similar process as in the buffet case. In the end the model predicts that insurance markets shouldn't exist.

So insurance shouldn't exist and neither should buffets. And yet both do. So why is this? In the case of insurance, one common explanation (described here by this year's John Bates Clark winner Amy Finkelstein) is risk aversion is sometimes correlated with low risk. This means that people differ in how much they value being insured against bad outcomes, and those who value insurance the most also happen to be those who have low expected costs. You know this kind of person: very safe people who take few risks, are very responsible, and also very healthy. You also know risk takers who are likely to be crippled in a hangliding accident or mauled by a bear (because they were taunting it as part of some extreme sport) but are more likely than most to be uninsured even though healthcare companies would likely undercharge them for insurance since they don't know what ridiculous risk takers they are (unless they've been injured in high risk accidents before; "tell me again how you lost your foot?" "shark surfing, sir").

But why is it that buffets can exist? They are subject to the same adverse selection problems, and even if they could tell who is going to overeat, the PR of turning away people who "look like they'll eat too much" isn't going to be worth it. Clearly the risk premium explanation does not apply here, since consumers have a good idea how much they are going to eat in advance, they aren't insuring against the probability they will be way more hungry than they thought in any meaningful sense. So tell me, dear reader, why is it that buffets do not succumb to the adverse selection problem and cease to exist? Why aren't there more Bill Wisths?